1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Fofino [41]
2 years ago
6

Inverse of f(x)=2 1/2-3 1/3x and what is its x intercept

Mathematics
2 answers:
zaharov [31]2 years ago
8 0

Find appropriate f(x) first

  • 2 1/2=5/2
  • 3 1/3=10/3

Now

  • y=-10/3x+5/2

So

InterchAnge x and y

  • x=-10/3y+5/2

Find y which is the inverse

  • x-5/2=-10/3y
  • y=-3/10x+5/2×3/10
  • y=-3/10x+3/4

x intercept

  • 10/3x+3/4=0
  • x=-3/4×3/10
  • x=-9/40

Graph attached

bearhunter [10]2 years ago
5 0

Answer:

\textsf{Inverse function}: \quad  f^{-1}(x)=\dfrac{3}{4}-\dfrac{3}{10}x

x\textsf{-intercept}:\quad\left(\dfrac{5}{2},0\right)

Step-by-step explanation:

Given:

f(x)=2\frac{1}{2}-3\frac{1}{3}x

Rewrite the function so it is a <u>rational function</u>

Convert the mixed numbers to improper fractions:

\implies f(x)=\dfrac{5}{2}-\dfrac{10x}{3}

Make the denominators the same:

\implies f(x)=\dfrac{3 \cdot 5}{3\cdot 2}-\dfrac{2 \cdot 10x}{2 \cdot 3}

\implies f(x)=\dfrac{15}{6}-\dfrac{20x}{6}

Combine:

\implies f(x)=\dfrac{15-20x}{6}

The inverse of a function is its <u>reflection in the line y = x</u>

To <u>find the inverse</u>, make x the subject

Replace f(x) with y:

\implies y=\dfrac{15-20x}{6}

\implies 6y=15-20x

\implies 6y-15=-20x

\implies x=\dfrac{-6y+15}{20}

\implies x=\dfrac{15-6y}{20}

Replace x with f^{-1}(x) and y with x:

\implies f^{-1}(x)=\dfrac{15-6x}{20}

If necessary, convert back into the same format as the original function:

\implies f^{-1}(x)=\dfrac{15}{20}-\dfrac{6x}{20}

\implies f^{-1}(x)=\dfrac{3}{4}-\dfrac{3}{10}x

The x-intercept of the inverse function is the point at which it crosses the x-axis, so when f^{-1}(x)=0

\implies \dfrac{15-6x}{20}=0

\implies 15-6x=0

\implies 6x=15

\implies x=\dfrac{15}{6}=\dfrac{5}{2}

Therefore, the x-intercept is:

\left(\dfrac{5}{2},0\right)

You might be interested in
Can someone plz help me ASAP thxs
allsm [11]

Answer:

352

Step-by-step explanation:

8 x 6 x 8 = 384

384- (4 x 1 x 8)

384-32=352

6 0
3 years ago
Simplify:(y²+z²) -2yz​
VMariaS [17]

Answer:

  (y-z)^{2}

Step-by-step explanation:

  (y^{2}+z^{2} ) -2yz\\\\y^{2} +z^{2} - 2yz\\\\y^{2} +2yz + z^{2}\\\\(y-z)^2\\

5 0
3 years ago
The price of one share of Acme Company declined $5 per day for 4 days in a row. How much did the price of one share change in th
Ksju [112]
If the price went down $5 per day for four days straight, then it would have went down $20 total after the four days.
7 0
3 years ago
Read 2 more answers
4. In the diagram below, TUVW is a rectangle. Prove ^TZW=^UZV.
navik [9.2K]
Tzw uzv in the diagram bellow is a rectangle
5 0
3 years ago
Which of the following is NOT approximately equivalent to one of the metric units
dmitriy555 [2]

Answer:

Poundsis not equivalent to one of the metric units, that is WEIGHT.

5 0
3 years ago
Other questions:
  • 9y-36=-15x in Slope intercept form
    9·2 answers
  • A man walks 10 miles in x hours. How far does he walk in one hour?
    7·1 answer
  • Urgent help needed w/ right triangle trig
    8·1 answer
  • Question 1
    10·1 answer
  • P(x)=58x−311
    8·2 answers
  • A searchlight rotates through one complete revolution every 4 seconds. How long does it take the light to rotate through 90 degr
    9·2 answers
  • Approximate which two integers √210 is between.<br>​
    6·1 answer
  • What does 2x-y^3 equal?
    10·1 answer
  • Answer please due this second
    11·1 answer
  • In ΔTUV, v = 240 inches, t = 390 inches and ∠U=71°. Find the area of ΔTUV, to the nearest square inch.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!